Solve for x 2 square root of 5 = square root of x

$2 \sqrt{5} = \sqrt{x}$

Step 1

Rewrite the equation as $\sqrt{x} = 2 \sqrt{5}$ .

$\sqrt{x} = 2 \sqrt{5}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = {(2 \sqrt{5})}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = {(2 \sqrt{5})}^{2}$

Simplify the left side.

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5})}^{2}$

Rewrite the expression.

$x^{1} = {(2 \sqrt{5})}^{2}$

Simplify.

$x = {(2 \sqrt{5})}^{2}$

Simplify the right side.

Simplify ${(2 \sqrt{5})}^{2}$ .

Simplify the expression.

Apply the product rule to $2 \sqrt{5}$ .

$x = 2^{2} {\sqrt{5}}^{2}$

Raise $2$ to the power of $2$ .

$x = 4 {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$x = 4 {(5^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = 4 \cdot 5^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x = 4 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = 4 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$x = 4 \cdot 5^{1}$

Evaluate the exponent.

$x = 4 \cdot 5$

Multiply $4$ by $5$ .

$x = 20$

Solve for x 2 square root of 5 = square root of x

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